A certain class of analytic functions of complex order connected with a q-analogue of integral operators

Srivástava, H. M.; El-Deeb, Sheza M.

doi:10.18514/mmn.2020.3102

Cited by 19 publications

(14 citation statements)

References 15 publications

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“…In this survey-cum-expository review article [13], the mathematical explanation and applications of the fractional q-calculus and the fractional q-derivative operators in geometric function theory were systematically investigated. For some more recent investigations about the recent usages of the q-calculus in geometric function theory, we may refer the interested readers to [14][15][16][17][18][19][20][21][22][23][24][25][26][27]. Definition 5.…”

Section: Definitionmentioning

confidence: 99%

Coefficient Estimates for a Subclass of Analytic Functions Associated with a Certain Leaf-Like Domain

et al. 2020

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First, by making use of the concept of basic (or q-) calculus, as well as the principle of subordination between analytic functions, generalization Rq(h) of the class R(h) of analytic functions, which are associated with the leaf-like domain in the open unit disk U, is given. Then, the coefficient estimates, the Fekete–Szegö problem, and the second-order Hankel determinant H2(1) for functions belonging to this class Rq(h) are investigated. Furthermore, similar results are examined and presented for the functions zf(z) and f−1(z). For the validity of our results, relevant connections with those in earlier works are also pointed out.

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Section: Definitionmentioning

confidence: 99%

Coefficient Estimates for a Subclass of Analytic Functions Associated with a Certain Leaf-Like Domain

et al. 2020

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“…This remark by Srivastava [27] will certainly utilize any attempt to create the quite simple (p, q)-variations of the outcomes, which we have provided in this article. These observations have already been addressed in many papers, as seen in [28][29][30].…”

Section: Discussionmentioning

confidence: 74%

A Generalized Class of Functions Defined by the q-Difference Operator

Andrei

Caus

2021

Symmetry

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The goal of the present investigation is to introduce a new class of analytic functions (Kt,q), defined in the open unit disk, by means of the q-difference operator, which may have symmetric or assymetric properties, and to establish the relationship between the new defined class and appropriate subordination. We derived relationships of this class and obtained sufficient conditions for an analytic function to be Kt,q. Finally, in the concluding section, we have taken the decision to restate the clearly-proved fact that any attempt to create the rather simple (p,q)-variations of the results, which we have provided in this paper, will be a rather inconsequential and trivial work, simply because the added parameter p is obviously redundant.

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“…In references ( [12][13][14][15][16][17][18][19][20]) can be found similar studies on analytical functions in recent years.…”

Section: Making Use Of the Binomial Series Formentioning

confidence: 96%

Coefficient estimates for certain subclasses of analytic functions defined by new operator

Bayram

Yalçın

2021

Fourth International Conference of Mathematical Sciences (Icms 2020)

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The study of operators plays an essential role in Mathematics, especially in Geometric Function Theory in Complex Analysis and its related fields. Many derivative and integral operators can be written in terms of convolution of certain analytic functions. The class of analytic functions, which has an essential place in the theory of geometric functions, has been studied by many researchers before. This topic still maintains its popularity today. In this paper, we investigate certain subclasses of analytic functions defined by generalized differential operators involving binomial series. Also, we obtain coefficient estimates involving of the nonhomogeneous Cauchy-Euler differential equation of order .

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A certain class of analytic functions of complex order connected with a q-analogue of integral operators

Cited by 19 publications

References 15 publications

Coefficient Estimates for a Subclass of Analytic Functions Associated with a Certain Leaf-Like Domain

Coefficient Estimates for a Subclass of Analytic Functions Associated with a Certain Leaf-Like Domain

A Generalized Class of Functions Defined by the q-Difference Operator

Coefficient estimates for certain subclasses of analytic functions defined by new operator

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